Improvements in the field of power electronics and the complexity of modern control systems increase the demands of asynchronous motors in variable speed electric actuators, because of their robustness and efficiency. Traditionally asynchronous machines have been used in electric power plants, essentially in applications wherein the stator winding is connected to the distribution mains. Typical applications of asynchronous machines are in wind or water driven power plants or combined heat and power generation plants (CHP).
The reasons of this traditionally restricted field of use is that asynchronous machines do not have an excitation winding and thus they require an initial magnetization for starting power generation and a reactive power source for sustaining the magnetic induction field during operation. Moreover, when an asynchronous machine supplies a passive network, the frequency of the output voltage is not tied to the rotation speed of the shaft, as in synchronous machines.
To better understand the addressed problem, the functioning principles of asynchronous machines are briefly explained. An asynchronous motor functions as a power generator when the absorbed electric power and the mechanical power applied to the shaft of the machine are both negative.
From a mechanical point of view, this means that a torque must be applied to the shaft of the machine for generating power. Depending on the applications, either a thermal motor, a gas turbine, the vanes of an wind or water turbine or even another electrical motor provides such a torque. From an electric point of view, to render negative the electrical power absorbed by the asynchronous machine, the real part of the impedance of the machine that may be calculated by solving the well-known equivalent circuit depicted in FIG. 1, to be less than zero.
This condition is verified, with a good approximation, for a slip σ ranging from 0 and −1. By definition:
  σ  =            ω      -              p        ⁢                                  ⁢                  ω          r                      ω  with ω being the angular frequency of the voltage and/or of the stator current, p the number of polar pairs and ωr the rotation speed of the shaft of the machine, this happens for rotation speeds larger than the synchronism speed ωs
      ω    s    =      ω    p  This functioning condition is called “hyper-synchronism”.
When the power plant is connected to the mains, the output voltage of the machine and its frequency are imposed. When the power plant is isolated from the mains, the generated voltage and frequency are not so forced and regulating them is not easy. Indeed, the frequency is not directly correlated with the rotation speed of the machine, but with the slip and thus by load conditions. Moreover, it is not possible to regulate the voltage by modifying the excitation, because there is no such input in asynchronous machines.
For maintaining the induction field in the magnetic gap it is necessary to use a reactive power source. This may be done by coupling a bank of capacitors to the system.
From these consideration, it is clear that the sole condition that ensures a sinusoidal steady state at the desired frequency is that the sum of the load impedance is null, including an excitation capacitance C connected in parallel to a load resistance RL (in the case of purely Ohmic load), and the impedance of the machine, i.e.:
                                                                                                              ℜe                    ⁢                                          {                                                                        Z                          .                                                machine                                            }                                                        =                                      ℜe                    ⁢                                          {                                                                        Z                          .                                                load                                            }                                                                                                                                                                𝔍                    ⁢                                                                                  ⁢                    m                    ⁢                                          {                                                                        Z                          .                                                machine                                            }                                                        =                                      𝔍                    ⁢                                                                                  ⁢                    m                    ⁢                                          {                                                                        Z                          .                                                load                                            }                                                                                                    }                ⇒                                                                                                  R                    s                                    +                                                            σ                      ⁢                                                                                          ⁢                                              ω                        2                                            ⁢                                              L                        m                        2                                            ⁢                                              R                        r                        ′                                                                                                            R                        r                                                  ′                          2                                                                    +                                                                        σ                          2                                                ⁢                                                  ω                          2                                                ⁢                                                  L                          r                                                      ′                            2                                                                                                                                              =                                  -                                                            R                      L                                                              1                      +                                                                        ω                          2                                                ⁢                                                  R                          L                          2                                                ⁢                                                  C                          2                                                                                                                                                                                                                                  ω                    ⁢                                                                                  ⁢                                          L                      s                                                        -                                                                                    σ                        2                                            ⁢                                              ω                        3                                            ⁢                                              L                        m                        2                                            ⁢                                              L                        r                        ′                                                                                                            R                        r                                                  ′                          2                                                                    +                                                                        σ                          2                                                ⁢                                                  ω                          2                                                ⁢                                                  L                          r                                                      ′                            2                                                                                                                                              =                                                      ω                    ⁢                                                                                  ⁢                                          R                      L                      2                                        ⁢                    C                                                        1                    +                                                                  ω                        2                                            ⁢                                              R                        L                        2                                            ⁢                                              C                        2                                                                                                                                                    (        1        )            wherein Żmachine is the impedance of the machine, Żload is the load impedance, Rs is the resistance of the stator windings, R′r the resistance of the rotor “seen” from the stator, σ is the slip, RL is the load resistance, C is the capacitance of the excitation bank of capacitors, Ls is the stator leakage inductance and Lm is the magnetization inductance of the machine.
The system described in Eq. (1) includes two algebraic equations involving four variables σ, ω, C e RL. To have a singular solution, it is necessary to establish two of the four variables. Normally, these two variables are ω and RL because usually the load is readily established and the frequency must be constant and of a standard value (in Europe 50 Hz). The values of the capacitance C and of the slip a may thus be calculated.
According to this approach, the rotation speed does not depend on the torque applied to the shaft of the generator. This condition is verified because the equations (1) hold in the hypothesis that Lm be constant.
If magnetic nonlinearities are considered, the value of Lm depends on the magnetization current and thus on the value of the torque. As a consequence, there is a functional connection between the rotation speed and the applied torque.
For establishing the nominal voltage, it is possible to impose that the electromagnetic torque Tel and the mechanical torque Tm be equal at steady state conditions:
                              T          el                =                              T            m                    =                                    3              2                        ⁢                                                            pL                  m                                ⁡                                  (                                      V                                                                  Z                        .                                            load                                                        )                                            2                        ⁢                                          σ                ⁢                                                                  ⁢                ω                ⁢                                                                  ⁢                                  R                  r                  ′                                ⁢                                  L                  m                                                                              R                  r                                      ′                    2                                                  +                                                      σ                    2                                    ⁢                                      ω                    2                                    ⁢                                      L                    r                                          ′                      ⁢                                                                                          ⁢                      2                                                                                                                              (        2        )            From the above considerations, the absolute value of the load impedance, and also the slip σ and the angular frequency ω, is determined once equations (1) are solved. Substituting the variable V with the desired voltage value, the torque to be applied to the asynchronous generator is determined.
A linear analysis, shows how the generated voltage and frequency depend on the torque and the capacitance. Typically, Lm is considered constant, thus the generated voltage depends on the torque Tm and the frequency depends on the capacitance C.
Literature describes asynchronous power generation systems in which voltage and frequency regulation are linearly implemented. Usually, the voltage is controlled by varying the total capacitance connected to the output line using a bank of capacitors individually connected into the circuit either electromechanically by contactors or electronically by using so-called “statcom” devices. Statcoms are devices that vary the impedance “seen” from the input nodes by configuring their switches. The frequency is controlled by adjusting the motor speed or by introducing a two-stage frequency converter between the asynchronous generator and the load.
A power plant that uses an asynchronous generator moved by a motor for supplying a load is depicted in FIG. 3. The functional blocks are identified by an identification number and a qualitative description of their functioning follows.
Block 1—Asynchronous Generator
The functioning of the asynchronous generator is determined by the following algebraic-differential equations:
                    {                                                                                                              ⁢                                                                            v                      _                                        s                                    =                                                                                    R                        s                                            ·                                                                        i                          _                                                s                                                              +                                                                  L                        s                                            ⁢                                                                        ⅆ                                                                                                                                                          ⅆ                          t                                                                    ⁢                                                                        i                          _                                                s                                                              +                                                                  L                        m                                            ⁢                                                                        ⅆ                                                                                                                                                          ⅆ                          t                                                                    ⁢                                              (                                                                                                            i                              _                                                        r                            ′                                                    ⁢                                                      ⅇ                                                          j                              ⁢                                                                                                                          ⁢                              p                              ⁢                                                                                                                          ⁢                              θ                                                                                                      )                                                                                                                                                                    0                =                                                                            R                      r                      ′                                        ·                                                                  i                        _                                            r                      ′                                                        +                                                            L                      r                      ′                                        ⁢                                                                  ⅆ                                                                                                                                              ⅆ                        t                                                              ⁢                                                                  i                        _                                            r                      ′                                                        +                                                            L                      m                                        ⁢                                                                  ⅆ                                                                                                                                              ⅆ                        t                                                              ⁢                                          (                                                                                                    i                            _                                                    s                                                ⁢                                                  ⅇ                                                                                    -                              j                                                        ⁢                                                                                                                  ⁢                            p                            ⁢                                                                                                                  ⁢                            θ                                                                                              )                                                                                                                                                                J                  ⁢                                                            ⅆ                      2                                                              ⅆ                                              t                        2                                                                              ⁢                                                                          ⁢                  θ                                =                                                      T                    el                                    -                                      T                    m                                                                                                                                            T                  el                                =                                                      3                    2                                    ⁢                                      p                    ·                                          L                      m                                                        ⁢                  𝔍                  ⁢                                                                          ⁢                  m                  ⁢                                      {                                                                                            i                          _                                                s                                            ⁢                                                                                                    i                            r                            ′                                                    ⋓                                                _                                                              }                                                                                                          (        3        )            wherein:                vs=symmetrical component of the stator voltage;        is=symmetrical vector component of the stator current;        i′r=symmetrical vector component of the rotor current seen from the stator;        Rs=stator resistance;        R′r=rotor resistance seen from the stator;        Ls=rotor leakage inductance;        L′r=rotor leakage inductance seen from the stator;        Lm=magnetization inductance;        J=moment of inertia of the group;        θ=instant position of the reference integral with the rotor in respect to the inertial reference;        p=polar pairs;        Tel=electromagnetic torque; and        Tm=motor torque.        
To make the asynchronous machine operate as a generator, the following inequalities must be satisfied:Tel<0 and Tm<0.By analyzing the mathematical model, the system of equations (3) includes two differential vectorial equations and one algebraic vectorial equation, but includes three vectorial variables (vs, is, i′r) and a scalar variable (θ).
The variables are determined by considering together equations (3) with equations (1) that describe the functioning of the power plant. When the plant is connected to the mains, a vectorial condition is introduced by specifying the module and the phase of the symmetric voltage component, as imposed by the mains.
Block 2—Motor
The motor PRIME MOVER is functionally represented as a block input with a signal coming from the control circuit for applying a corresponding torque (Tm) to the shaft of the asynchronous generator. As a matter of fact, the torque Tm may be constant, for example, by approximately considering the torque-speed characteristic of an engine in a certain range, or it may be a function of a certain parameter of the power generation plant (for example the speed). This naturally depends on the type of the prime mover.
Block 3—Electric Load and Excitation Group
This functional block may be described as shown in FIG. 4, wherein                is is the symmetric component of the stator current;        ic is the current of the excitation group;        iL is the load current;        C is the capacitance of the excitation group;        LL is the load inductance;        RL is the load resistance; and        V is the symmetric component of the stator voltage.        
The functioning of the circuit of FIG. 4 may be described by the following system of differential equations:
                                                        ⅆ                              V                _                                                    ⅆ              t                                =                      -                                                                                i                    _                                    s                                +                                                      i                    _                                    L                                            C                                      ⁢                                  ⁢                                            ⅆ                                                i                  _                                L                                                    ⅆ              t                                =                                                    1                                  L                  L                                            ⁢                              V                _                                      -                                                            R                  L                                                  L                  L                                            ⁢                                                i                  _                                L                                                                        (        4        )            These two equations, together with equations (3) allow solving the system of differential equations when the system is isolated from the mains. The excitation group, schematically represented by the capacitance C of FIG. 4, must be capable of delivering a reactive power that varies as a function of the needs of the asynchronous generator and of the load. For this reason the capacitance connected to the output line must be adjustable.Block 4—Control Circuit
It is the functional block that corrects the capacitance and torque values for regulating the generated voltage and its frequency.
Block 5—Remote Control Switches
Remote control switches select the functioning mode of the power plant: from the “grid-connected” mode (switches closed) to the “isolated” mode (switches open) or vice versa. Through special studies, the Applicant found that the commonly used separate control for voltage and for frequency, as illustrated in FIG. 5, could lead to conditions of instability or to excessively long transients before reaching the desired values because of interference between the two controllers (VMAX CONTROLLER, FREQ CONTROLLER). Moreover, such a control may not be sufficiently precise because the real system is magnetically nonlinear. It is well known that there are functioning conditions of an asynchronous generator at which the saturation of magnetic circuits contributes to limit the output voltage.